LPCVD Reaction Kinetics
Low Pressure CVD operates at reduced pressures (0.1-1 Torr) enabling better uniformity and step coverage through mean free path control and surface reaction kinetics.
Arrhenius Rate Equation
k = k₀ × exp(-Ea / RT)
where:
k: rate constant (cm/s)
k₀: pre-exponential factor (10⁶-10¹⁰ cm/s)
Ea: activation energy (30-60 kcal/mol for Si₃N₄)
R: gas constant (1.987 cal/mol·K)
T: temperature (K)
Surface Reaction Rate
r = k × P^n × θ_vacant
r: growth rate (nm/min)
P: partial pressure (Torr)
n: reaction order (0.5-2.0)
θ_vacant: fraction of vacant surface sites
Mass Transport Limited Rate
r_transport = h_m × (C_bulk - C_surface)
h_m: mass transfer coefficient = D/δ
D: diffusion coefficient ∝ T^1.5 / P
δ: boundary layer thickness
Regime Transition - Damköhler Number
Da = k_surface / k_transport
Da << 1: Surface reaction limited (high T)
→ Strong temperature dependence
→ Ea_apparent = Ea_reaction
Da >> 1: Mass transport limited (low T)
→ Weak temperature dependence
→ Ea_apparent ≈ 2-5 kcal/mol
Wafer Loading Effect
Depletion = 1 - exp(-N_wafers × A_wafer × k / Q)
N_wafers: number of wafers in batch
A_wafer: wafer surface area (cm²)
Q: volumetric flow rate (cm³/s)
Higher loading → more depletion → non-uniformity
Temperature Profile in Tube
T(x) = T_set - ΔT_end × [(x/L)² + (x/L)⁴]
Typical ΔT: 5-20°C across 100 cm tube
Affects uniformity through k(T) variation
LPCVD Silicon Nitride
3 SiH₂Cl₂ + 4 NH₃ → Si₃N₄ + 6 HCl + 6 H₂
Typical conditions:
Temperature: 700-850°C
Pressure: 200-400 mTorr
DCS:NH₃ ratio: 1:4 to 1:6
Growth rate: 3-10 nm/min
Thickness Uniformity
Uniformity (%) = (1 - σ/μ) × 100
σ: standard deviation of thickness
μ: mean thickness
LPCVD typically achieves >95% uniformity
vs. 85-90% for APCVD